Abstract
We prove Kronecker's first limit formula for cofinite discrete subgroups of SL$(2,\mathbbC)$, also called Kleinian groups, generalizing a method of Goldstein over SL$(2,\mathbb R)$. The proof uses the Fourier expansion of Eisenstein series, leading to an analogue of the logarithm of the Dedekind eta function, and whose transformation law produces a function analogous to the one related to Dedekind sums. We derive several basic properties of this new function.
Citation
Zihan Miao. Anh Nguyen. Tian An Wong. "Kronecker's first limit formula for Kleinian groups." Funct. Approx. Comment. Math. 69 (1) 7 - 25, September 2023. https://doi.org/10.7169/facm/1997
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